Wireless acoustic sensor networks represent an attractive solution that can be deployed for animal detection and recognition in a monitored area. A typical configuration for this application would be to transmit the whole acquired audio signal through multi-hop communication to a remote server for recognition. However, continuous data streaming can cause a severe decline in the energy of the sensors, which consequently reduces the network lifetime and questions the viability of the application. An efficient solution to reduce the sensor's radio activity would be to perform the recognition task at the source sensor then to communicate the result to the remote server. This approach is intended to save the energy of the acoustic source sensor and to unload the network from carrying, probably, useless data. However, the validity of this solution depends on the energy efficiency of performing on-sensor detection of a new acoustic event and accurate recognition. In this context, this paper proposes a new scheme for on-sensor energy-efficient acoustic animal recognition based on low-complexity methods for feature extraction using the Haar wavelet transform. This scheme achieves more than 86% in recognition accuracy while saving 71.59% of the sensor energy compared with the transmission of the raw signal.